Indeed. If only the people decide, who holds bitcoin, why wouldn't they abolish the coinbase tx completly, I mean now.
Well, no miner is forced to claim the block reward subsidy. So anyone can start reducing the amount of bitcoins (and thus increasing the value of existing bitcoins) by mining (solo) but not claiming the subsidy.
Now if you are suggesting to change the protocol so that starting with the next block (or at some point in the future) there is no more block reward subsidy, you can try that right now. You just change one line of code and release your hard-fork variant of the Bitcoin-Qt/bitcoind client and start a campaign to get the economic majority to switch to using it.
Users aren't stupid though -- they know that fees are insufficient currently to incent enough miners to protect the network. So adopting your fork would be crypto-currency suicide. So the limit stays at 25 BTC per block, until block 420,000 and then 12.5 BTC per block, until block 630,000 and then 6.25 per block, etc.
Now let's say it is year 2024 and fees alone are seen as being way more than sufficient enough to support the level of hashing necessary to protect the network, so the fear of the loss of subsidy impacting hashing capacity is not a limiting factor. However, people who hold bitcoins include people who have lent their coins out to those who have borrowed bitcoins and need to repay loans (denominated in bitcoins).
Presumably anyone borrowing bitcoins would require a clause in the loan agreement that if the subsidy were to be reduced (change in the money supply were to occur) that their principal and/or interest would be adjusted appropriately. If the subsidy is discontinued there would be little gain for those who have lent out their coins. And who lends bitcoins? The economic majority, that's who. So it is not in the best interest of any of the economic majority to change the rules as far as the rate of Bitcoin issuance -- towards either direction up or down.
[Edited: for clarity and readability]